Finite Group Databasebeta

← #21433640

Subgroups — #21433640

Order 7552.

504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273753C211yesmaximal, characteristic, complemented
2C2×#14273749C211yesmaximal, characteristic, complemented
3#16837969C211yesmaximal, characteristic, complemented
4#16837883C211yesmaximal, characteristic, complemented
5#16837623C212yesmaximal, complemented
6#16837616C212yesmaximal, complemented
7#16837601C212yesmaximal, complemented
8#16837596C212yesmaximal, complemented
9#16837428C211yesmaximal, characteristic, complemented
10#16837401C211yesmaximal, characteristic, complemented
11C2×#102×C59C211yesmaximal, characteristic, complemented
12C2×#11745685C2211yescharacteristic
13C2×#11745685C2211yescharacteristic
14#14273753—24no—
15#14273749—24no—
16C2×Dic236C2211yescharacteristic, complemented
17C2×#11745660C2211yescharacteristic, complemented
18C2×#11745660C2211yescharacteristic, complemented
19C2×#11745670C2212yes—
20C2×D472C2211yescharacteristic, complemented
21C2×#11745669C2212yes—
22C2×#11745664C2211yescharacteristic
23#14273723C2212yes—
24#14273714C2212yes—
25#14273698—21no—
26#14273698—21no—
27#14273696—22no—
28#14273692C2212yescomplemented
29#14273689C2212yescomplemented
30C4×C22⋊D59—22no—
31#14273686C2211yescharacteristic
32#14273685—21no—
33C4⋊C4×D59—21no—
34Dic59⋊C8C2212yescomplemented
35Dic59⋊C8C2212yescomplemented
36#14273650C2212yescomplemented
37#14273647C2212yescomplemented
38C22×D4×C59C2211yescharacteristic
39C22×C8×C59C2211yescharacteristic
40C2×C4⋊C4×C59C2211yescharacteristic
41#102×C59C2212yes—
42#102×C59C2212yes—
43C24×C59—21no—
44C2×D4×C59—22no—
45C2×D4×C59—21no—
46C2×D4×C59—22no—
47C2×D4×C59C2312yes—
48C22×C4×C59—21no—
49C22×C4×C59C2311yescharacteristic
50C2×C22⋊D59—21no—
51C2×C22⋊D59—21no—
52C2×C22⋊D59—22no—
53C2×C22⋊D59—22no—
54#11745685—22no—
55#11745685—22no—
56#11745685—22no—
57#11745685D414yescomplemented
58C2×D236C2311yescharacteristic
59C2×D236C2311yescharacteristic
60C2×C4×D59—21no—
61C2×C4×D59—21no—
62C2×C4×D59—22no—
63C2×Dic118C2311yescharacteristic
64C2×Dic118C2311yescharacteristic
65C2×C8×C59—22no—
66C2×C8×C59C2311yescharacteristic
67C2×C8×C59C2311yescharacteristic
68C4⋊C4×C59—21no—
69C4⋊C4×C59C2312yes—
70C22⋊Dic59—22no—
71C22⋊Dic59—22no—
72C22⋊Dic59D412yes—
73#11745670—24no—
74#11745669—24no—
75(C2×D59)⋊C4—22no—
76C4⋊Dic59D411yescharacteristic
77C4⋊Dic59D411yescharacteristic
78Dic59⋊C4—22no—
79C4×Dic59—22no—
80C4×Dic59C2312yes—
81#11745664—22no—
82C2×C59⋊C8C2312yes—
83Dic236—22no—
84D472—22no—
85#11745660—22no—
86#11745660—22no—
87C23×C59—22no—
88C23×C59—42no—
89C23×C59—81no—
90C23×C59—81no—
91C23×C59C2×D411yescharacteristic
92C22×D59—21no—
93C22×D59—21no—
94D4×C59—22no—
95D4×C59—22no—
96D4×C59—42no—
97C2×C4×C59—22no—
98C2×C4×C59—81no—
99C2×C4×C59C2×D411yescharacteristic
100C2×C4×C59C2×D412yes—
101C2×C4×C59#4112yes—
102C2×C4×C59C2411yescharacteristic
103C22⋊D59—24no—
104C22⋊D59—42no—
105C22⋊D59—82no—
106C22⋊D59—82no—
107C2×Dic59—21no—
108C2×Dic59—21no—
109C2×Dic59C2×D412yes—
110C2×Dic59C2×D412yes—
111D236—21no—
112D236—21no—
113D236—21no—
114D236C2×D412yes—
115C4×D59—24no—
116C4×D59—42no—
117C4×D59—82no—
118Dic118—21no—
119Dic118—21no—
120Dic118—21no—
121Dic118C2×D412yes—
122C8×C59—21no—
123C8×C59—21no—
124C59⋊C8—22no—
125C22×C59—21no—
126C22×C59—21no—
127C22×C59—42no—
128C22×C59—42no—
129C22×C59—42no—
130C22×C59—84no—
131C22×C59#12112yes—
132C22×C59C22×D411yescharacteristic
133C2×D59—22no—
134C2×D59—41no—
135C2×D59—41no—
136C2×D59—41no—
137C2×D59—41no—
138C2×D59—41no—
139C4×C59—42no—
140C4×C59#12112yes—
141C4×C59C22×D411yescharacteristic
142C4×C59C2×#4111yescharacteristic
143Dic59—22no—
144Dic59—22no—
145Dic59—22no—
146Dic59—41no—
147#3045—591nomaximal, Sylow
148C2×C59—22no—
149C2×C59—82no—
150C2×C59C2×#12111yescharacteristic
151C2×C59#57611yescharacteristic
152C2×C59#57711yescharacteristic
153D59—42no—
154D59—81no—
155C2×AGL(1,ℤ/8)—591no—
156C2×#135—591no—
157#535—591no—
158#520—591no—
159#464—592no—
160#463—592no—
161#460—592no—
162#459—592no—
163#424—591no—
164#417—591no—
165C2×#102D5911yescharacteristic, complemented
166C59#304511yescharacteristic, complemented, Sylow
167C2×#41—591no—
168C2×#41—591no—
169C22×D4C2×D5911yescharacteristic
170AGL(1,ℤ/8)—1184no—
171#135—1184no—
172C2×Q16—591no—
173C2×SD16—592no—
174C2×SD16—591no—
175C2×SD16—591no—
176C2×D8—592no—
177C2×D8—591no—
178C2×M16—591no—
179C22×C8C2×D5911yescharacteristic
180#127—592no—
181#124—592no—
182#121—1181no—
183#121—1181no—
184#120—1182no—
185C4×Q8—592no—
186C4×D4—592no—
187C4×D4—1182no—
188#117—591no—
189#117—1181no—
190C2×C4⋊C4—1181no—
191C2×C4⋊C4C2×D5911yescharacteristic
192C4⋊C8—592no—
193C4⋊C8—592no—
194#103—592no—
195#102—592no—
196#102C2×D5912yes—
197#102C2×D5912yes—
198C24—21no—
199#41—594no—
200#41—1182no—
201#41—1182no—
202#41—1182no—
203C2×Q8—591no—
204C2×Q8—591no—
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—21no—
208C2×D4—591no—
209C2×D4—591no—
210C2×D4—1182no—
211C2×D4—1182no—
212C2×D4—1181no—
213C2×D4—1181no—
214C2×D4C22×D5912yes—
215C22×C4—21no—
216C22×C4—1182no—
217C22×C4—1181no—
218C22×C4—1181no—
219C22×C4C22×D5911yescharacteristic
220Q16—1182no—
221SD16—1182no—
222SD16—1182no—
223SD16—1184no—
224D8—1182no—
225D8—1184no—
226M16—1182no—
227C2×C8—22no—
228C2×C8—592no—
229C2×C8C22×D5911yescharacteristic
230C2×C8C22×D5911yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—591no—
233C4⋊C4—591no—
234C4⋊C4—1182no—
235C4⋊C4C22×D5912yes—
236C22⋊C4—592no—
237C22⋊C4—1182no—
238C22⋊C4—1182no—
239C22⋊C4—1182no—
240C42—592no—
241C42—1182no—
242C23—22no—
243C23—42no—
244C23—81no—
245C23—81no—
246C23—1181no—
247C23—1181no—
248C23D4×D5911yescharacteristic
249Q8—592no—
250Q8—1181no—
251Q8—1181no—
252Q8—1181no—
253D4—22no—
254D4—22no—
255D4—42no—
256D4—592no—
257D4—1184no—
258D4—1181no—
259D4—1181no—
260D4—1181no—
261D4—4722no—
262D4—4722no—
263D4—2362no—
264C2×C4—22no—
265C2×C4—81no—
266C2×C4—592no—
267C2×C4—592no—
268C2×C4—1181no—
269C2×C4—1184no—
270C2×C4—1181no—
271C2×C4—4722no—
272C2×C4—2362no—
273C2×C4#1174568512yes—
274C2×C4D4×D5911yescharacteristic
275C2×C4D4×D5912yes—
276C2×C4C23×D5911yescharacteristic
277C8—21no—
278C8—21no—
279C8—1182no—
280C22—21no—
281C22—21no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—84no—
286C22—1182no—
287C22—2361no—
288C22—2361no—
289C22—2361no—
290C22—2361no—
291C22—2361no—
292C22#1427370012yes—
293C22C2×D4×D5911yescharacteristic
294C4—42no—
295C4—1182no—
296C4—1182no—
297C4—1182no—
298C4—2361no—
299C4#1427370012yes—
300C4C2×D4×D5911yescharacteristic
301C4C2×#1174568511yescharacteristic
302C2—22no—
303C2—82no—
304C2—4721no—
305C2—2362no—
306C2C2×#1427370011yescharacteristic
307C2#1683820311yescharacteristic
308C2#1683820811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#102×C59C2
socleC22×C59C22×D4
hypercenterC2×#102D59
hypocenterC59#3045
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14273753C2semidirect
2. C2×#14273749C2semidirect
3. #16837969C2semidirect
4. #16837883C2semidirect
5. #16837623C2semidirect
6. #16837616C2semidirect
7. #16837601C2semidirect
8. #16837596C2semidirect
9. #16837428C2semidirect
10. #16837401C2semidirect
11. C2×#102×C59C2semidirect
16. C2×Dic236C22semidirect
17. C2×#11745660C22semidirect
18. C2×#11745660C22semidirect
20. C2×D472C22semidirect
28. #14273692C22semidirect
29. #14273689C22semidirect
34. Dic59⋊C8C22semidirect
35. Dic59⋊C8C22semidirect
36. #14273650C22semidirect
37. #14273647C22semidirect
57. #11745685D4semidirect
165. C2×#102D59semidirect
166. C59#3045semidirect